(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
In the paper, an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed. The key idea is to use a Petrov-Galerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions. The inf-sup condition for P_1-P_0 triangular element (or Q_1-P_0 quadrilateral element) is established. And the optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.